"You do know they only accepted you because you're black?" reads a placard that forms part of the "I, too, am Oxford" campaign.

This week students have been raising awareness about the often overlooked issue of racial prejudice on campus. It started with Harvard's "I, too, am Harvard" photo project that went viral on social media.

Students at Oxford and Cambridge then followed suit, and drew attention to issues on their own campuses.

Those at Oxford say they want to "demonstrate that despite there being a greater number of students of colour studying at Oxford now than there has ever been before, there are still issues that need to be discussed."

They say they are "demanding that a discussion on race be taken seriously and that real institutional change occur".

Other comments those in the campaign had heard were: "Where are you really from?" and "I was pleasantly surprised you actually speak well".

So how much of a problem is racism on campus?

In 2011, a report by the National Union of Students (NUS) found that one in six black students had experienced racism at their institution, and one third did not trust their university to handle complaints properly.

A report by the York Student Think Tank this week revealed that one in ten students and workers at the University of York felt they had experienced some form of discrimination because of their race or ethnic background.

One in four from outside the EU said they felt discriminated against because of their race and half of respondents said they had witnessed racism happening to others. The kind of discrimination experienced included being stereotyped and treated differently.

Zena, a student who wishes to be known only by her first name, says: "I constantly have to deal with things like offensive racist 'banter' from white students, or assumptions on the basis of my ethnicity. And it's difficult to report it to support services.

"I commonly hear: 'where are you really from', as if the fact that I am ethnically Arabic must mean that I am lying about being a British citizen. It is difficult to know how to deal with comments like this, as I doubt any university would take a complaint seriously."

Elsewhere, students at the University of Edinburgh were accused of racism for dressing as Somali pirates as a fancy dress outfit. And the University of London students' union was criticised when a "blacked up" student won a fancy dress prize at an event held in the union.

So what is the best way to tackle the problem? Respondents in the York Vision report found it hard to call out instances of racism because they often "lack malice or a specific target".

Zena says: "It is difficult to speak up about racist jokes without being seen as too sensitive."

Isabelle Scott and Sairish Tahir, racial equality officers at the University of York's student union, say: "These issues will always be prevalent and unfortunately these statistics will rise, if not tackled by both unions and universities."

Do you think racism is a prominent issue on your campus? How should it be tackled? Share your thoughts and experiences in the comments section below.

• This article was amended on 14 March 2014 - it previously mentioned a "University of York" report, but the report was by York Student Think Tank. The article has been changed accordingly.